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A memristive Chua's circuit regarded as a paradigm is reconsidered to exhibit its extreme multistability in this Letter. Memristor initial state-dependent dynamics is analysed and the coexistence of infinitely many attractors related to memristor initial states is revealed by numerical simulations and circuit simulations. The dynamical behaviour just reflects the emergence of extreme multistability in the memristive circuit.

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High implementation complexity of multi-scroll circuit is a bottleneck problem in real chaos-based communication. Especially, in multi-scroll Chua's circuit, the simplified implementation of piecewise-linear resistors with multiple segments is difficult due to their intricate irregular breakpoints and slopes. To solve the challenge, this paper presents a systematic scheme for synthesizing a Chua's diode with multi-segment piecewiselinearity, which is achieved by cascading even-numbered passive nonlinear resistors with odd-numbered ones via a negative impedance converter. The traditional voltage mode op-amps are used to implement nonlinear resistors. As no extra DC bias voltage is employed, the scheme can be implemented by much simpler circuits. The voltage-current characteristics of the obtained Chua's diode are analyzed theoretically and verified by numerical simulations. Using the Chua's diode and a secondorder active Sallen-Key high-pass filter, a new inductor-free Chua's circuit is then constructed to generate multi-scroll chaotic attractors. Different number of scrolls can be generated by changing the number of passive nonlinear resistor cells or adjusting two coupling parameters. Besides, the system can be scaled by using different power supplies, satisfying the lowvoltage low-power requirement of integrated circuit design. The circuit simulations and hardware experiments both confirmed the feasibility of the designed system.